Optimal. Leaf size=10 \[ \text{CosIntegral}(x)-\frac{\sin (x)}{x} \]
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Rubi [A] time = 0.0254586, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 6, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.333, Rules used = {3297, 3302} \[ \text{CosIntegral}(x)-\frac{\sin (x)}{x} \]
Antiderivative was successfully verified.
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Rule 3297
Rule 3302
Rubi steps
\begin{align*} \int \frac{\sin (x)}{x^2} \, dx &=-\frac{\sin (x)}{x}+\int \frac{\cos (x)}{x} \, dx\\ &=\text{Ci}(x)-\frac{\sin (x)}{x}\\ \end{align*}
Mathematica [A] time = 0.0020751, size = 10, normalized size = 1. \[ \text{CosIntegral}(x)-\frac{\sin (x)}{x} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 11, normalized size = 1.1 \begin{align*}{\it Ci} \left ( x \right ) -{\frac{\sin \left ( x \right ) }{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [C] time = 1.06833, size = 20, normalized size = 2. \begin{align*} \frac{1}{2} \, \Gamma \left (-1, i \, x\right ) + \frac{1}{2} \, \Gamma \left (-1, -i \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.81588, size = 80, normalized size = 8. \begin{align*} \frac{x \operatorname{Ci}\left (-x\right ) + x \operatorname{Ci}\left (x\right ) - 2 \, \sin \left (x\right )}{2 \, x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 1.60248, size = 17, normalized size = 1.7 \begin{align*} - \log{\left (x \right )} + \frac{\log{\left (x^{2} \right )}}{2} + \operatorname{Ci}{\left (x \right )} - \frac{\sin{\left (x \right )}}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.07237, size = 18, normalized size = 1.8 \begin{align*} \frac{x \operatorname{Ci}\left (x\right ) - \sin \left (x\right )}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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